Self-Similarity Breeds Resilience

TL;DR

This paper explores how self-similarity in systems can lead to resilience against adversarial behaviors, formalizing the concepts and identifying classes of systems where resilience is decidable.

Contribution

It formalizes the notions of self-similarity, resilience, and adversaries using transition systems, and identifies a class of systems with decidable resilience properties.

Findings

Decidability of resilience for certain self-similar systems

Framework applicable to systems robust against failures and attacks

Illustrative examples demonstrate practical relevance

Abstract

Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system, adversary and resilience in operational terms, based on transition systems and observations. While the general problem of proving systems to be behaviourally self-similar is undecidable, we show, by casting them in the framework of well-structured transition systems, that there is an interesting class of systems for which the problem is decidable. We illustrate our prescriptive framework for resilience with some small examples, e.g., systems robust to failures in a fail-stop model, and those avoiding side-channel attacks.